Primary display changes after killing a non-cosmic session launched with cosmic-greeter

[whitespire]

Steps to reproduce:

1. Start up cosmic greeter on a laptop with an external display connected;
2. choose a non-cosmic session (tested with Hyprland);
3. kill the session: loginctl terminate-session 3 (or whatever is the number of the session you are in).

Result:

• The external display is now considered the primary;
• this change does not carry over to other sessions;
• this change persists between logouts and reboots;
• upon plugging the monitor in and out while inside the cosmic session the ordering returns to normal.

Here is screenshot of cosmic-settings showing the external display as primary:

Adding to that. after plugging the external monitor out and back in the number shown on the display in the settings app remains the same, although the displays changed their order, but this might be outside the scope of this particular issue.